1129_D. Isolation
Problem Description
Find the number of ways to divide an array a of n integers into any number of disjoint non-empty segments so that, in each segment, there exist at most k distinct integers that appear exactly once.
Since the answer can be large, find it modulo 998 244 353.
Input
The first line contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 10^5) — the number of elements in the array a and the restriction from the statement.
The following line contains n space-separated integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n) — elements of the array a.
Output
The first and only line contains the number of ways to divide an array a modulo 998 244 353.
Examples
Input
3 1 1 1 2
Output
3
Input
5 2 1 1 2 1 3
Output
14
Input
5 5 1 2 3 4 5
Output
16
Note
In the first sample, the three possible divisions are as follows.
- [[1], [1], [2]]
- [[1, 1], [2]]
- [[1, 1, 2]]
Division [[1], [1, 2]] is not possible because two distinct integers appear exactly once in the second segment [1, 2].
Contest Information
- Contest ID: 1129
- Problem Index: D
- Points: 2250.0
- Rating: 2900
- Tags: data structures, dp
- Time Limit: {'seconds': 3, 'nanos': 0} seconds
- Memory Limit: 256000000 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.